Cook potatoes according to directions on package. Place in refrigerator to cool while preparing the remaining ingredients.
Place peanut butter, chocolate chips, brown sugar and vanilla extract in a large saucepan. Heat over medium burner, stirring gently, until ingredients have melted and you have a smooth batter. Fold in cooled mashed potatoes until just blended.
Place in refrigerator and chill dough for 30 minutes. Dough should be firm but pliable at this point. Remove chilled dough and preheat oven to 375 degrees. Roll dough into small balls and place on greased cookie sheets. Press cookies flat with a fork. Bake at 375 for 8-10 minutes until golden brown. Cool for about 5 minutes before removing from cookie sheet.